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arXiv · 2604.19490

Verma Bases and Kashiwara-Nakashima Tableaux of $\mathfrak{sp}_4$

Bintao Cao·Ye Huang
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Abstract

We construct a one-to-one correspondence between the Verma basis vectors of a finite dimensional irreducible representation $L(\lambda)$ of the symplectic Lie algebra $\mathfrak{sp}_4$ and the Kashiwara-Nakashima tableaux of $\mathfrak{sp}_4$ with shape $\lambda $ naturally. We also give a proof of the linear independence of the Verma vector system directly.

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BibTeXRIS

Bintao Cao, Ye Huang. 2026-04-21. Verma Bases and Kashiwara-Nakashima Tableaux of $\mathfrak{sp}_4$. https://arxiv.org/abs/2604.19490

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